Let’s solve your question step by step, as requested, in **2 steps only** for each part: ### Given: - Beta (\(\beta\)) = 1.5 - Market return (\(r_m\)) = 16% - Risk-free rate (\(r_f\)) = 7% - (Note: You did not provide the cash flows for the project. I'll use placeholders \(CF_1, CF_2, \ldots\) in the formulas. Replace them with your actual numbers.) --- ## **a) Estimate the cost of capital for the project using CAPM** **Step 1:** CAPM formula: \[ \text{Cost of capital} = r_f + \beta (r_m - r_f) \] **Step 2:** Plug in the numbers: \[ = 7\% + 1.5 \times (16\% - 7\%) \] \[ = 7\% + 1.5 \times 9\% \] \[ = 7\% + 13.5\% = \boxed{20.5\%} \] --- ## **b) What is the project's present value?** **Step 1:** PV formula with the cost of capital (\(r = 20.5\%\)): \[ PV = \sum_{t=1}^{n} \frac{CF_t}{(1 + r)^t} \] **Step 2:** Plug in your cash flows (replace \(CF_t\) with actual numbers): \[ PV = \frac{CF_1}{1.205} + \frac{CF_2}{(1.205)^2} + \frac{CF_3}{(1.205)^3} + \cdots \] --- ## **c) What are the certainty-equivalent cash flows in each year?** **Step 1:** Certainty-equivalent cash flow (\(CE_t\)) formula: \[ CE_t = \frac{CF_t}{1 + \text{risk premium}} \] Here, risk premium = market risk premium \(\times\) beta \[ \text{Market risk premium} = r_m - r_f = 9\% \] \[ \text{Risk premium} = 1.5 \times 9\% = 13.5\% \] **Step 2:** Certainty-equivalent factor: \[ CE_t = \frac{CF_t}{1.135^t} \] --- ## **d) What is the ratio of the certainty-equivalent cash flows to the expected cash flows in each year?** **Step 1:** Ratio = \(\frac{CE_t}{CF_t}\) \[ \frac{CE_t}{CF_t} = \frac{1}{1.135^t} \] **Step 2:** For each year, - Year 1: \(1/1.135 = 0.881\) - Year 2: \(1/1.135^2 = 0.776\) - Year 3: \(1/1.135^3 = 0.684\) - etc. --- ## **e) Explain why this ratio declines?** **Step 1:** The ratio \(\frac{CE_t}{CF_t}\) declines over time because the certainty-equivalent factor \((1/1.135^t)\) gets smaller each year. **Step 2:** This reflects that the further in the future a cash flow is, the greater the risk and uncertainty, so we are willing to accept a lower "certain" value today for the same expected risky cash flow in the future. --- **Summary:** - a) Cost of capital: **20.5%** - b) Present value: \(\sum \frac{CF_t}{1.205^t}\) - c) Certainty-equivalent cash flow: \(\frac{CF_t}{1.135^t}\) - d) Ratio: \(1/1.135^t\) - e) The ratio declines because risk and uncertainty increase with time.